Hydrodynamics in graphene: Linear-response transport

We develop a hydrodynamic description of transport properties in graphene-based systems, which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this “three-mode” approximation, we evaluate transport coefficients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples, the macroscopic currents are inhomogeneous, which leads to a linear magnetoresistance in classically strong fields. Applying our theory to double-layer graphene-based systems, we provide a microscopic foundation for a phenomenological description of giant magnetodrag at charge neutrality and find the magnetodrag and Hall drag in doped graphene.

Figure 1

(Top) Magnetoresistance in graphene at charge neutrality. The uppermost curve shows the result (17) for a macroscopic sample. The lower curves show the result (45) for sample widths $W=100,20,10,2\mu \mathrm{m}$ (top to bottom). The results are calculated for realistic values of parameters: $T=240$ K, ${\tau }^{-1}=50$ K, ${\tau }_{ee}=0.2\tau ,{\tau }_{ph}=20\tau$. The inset illustrates the linear magnetoresistance for $W=0.1\mu \mathrm{m}$. The dashed line is a guide to the eye. (Bottom) Curvature of the above magnetoresistance in weak fields (in units of $\mathrm{k}\Omega /{\mathrm{T}}^2)$ as a function of $W$. Green line shows the prefactor in Eq. (17). The inset shows the region $W<1\mu \mathrm{m}$.

Figure 2

Schematic illustration of corrections to the Fermi-liquid predictions for the drag coefficient. The blue dashed curve represents the Fermi-liquid result ${\mathcal{R}}_D\sim T^2/{\mu }^2$. The green dotted curve represents the exponential approach to ${\mathcal{R}}_D$ within the two-mode approximation that retains the electric and imbalance currents. The red solid line shows the result (52) of the three-mode approximation approaching the Fermi-liquid regime as a power law in $T/\mu$.